It is well known the for optimum power transfer from a RFPS to a load an impedance-matching circuit is required. The output power of a CO2 gas discharge laser increases directly with increasing discharge volume. The RF input (load) impedance of the laser varies inversely as the output power and decreases directly as the area of the discharge. The load impedance can vary between lasers within the same model family due to variations in discharge gas pressure, spacing between the electrodes, and other factors
An impedance matching circuit may comprise by one or more LC networks consisting of one or more discrete inductors and capacitors, a length of transmission line or coaxial cable having a length which is a selected fraction of a wavelength long, or a plurality of fractional wavelength transmission lines in a selected arrangement.
An example 10A of an impedance-matching circuit including an inductive component and a capacitive component is schematically illustrated in FIG. 1A. Here, an RFPS 12 having an output impedance of 50 Ohms, represented as a resistor RS, is matched to a resistive load RL of 12 Ohms. In circuit 10A impedance matching is provided by a series inductor L and a parallel capacitor C. Values of L and C would be selected in accordance with the frequency of RFPS 12 as is known in the art. Impedance matching an RFPS in CO2 gas discharge lasers is described in detail in U.S. Pat. No. 7,540,779, assigned to the assignee of the present invention.
One example 10B of a prior-art impedance-matching circuit including a fractional wavelength transmission line is schematically illustrated in FIG. 1B. In this circuit, a transmission line section 14, having a length of one-quarter wavelength (λ/4) at the frequency of RFPS 12, is placed in series between RS and RL. RS and RL have values 65 Ohms and 50 Ohms respectively. For optimum impedance matching, λ/4 transmission line 14 has a characteristic impedance of 57 Ohms, i.e., (RS*RL)1/2, and introduces a phase-shift of 90° (π/2 radians) between the output of the RFPS and the input to the discharge electrodes.
Another example 10C of a prior-art impedance matching circuit including a fractional wavelength transmission line is schematically illustrated in FIG. 1C. Here there are two λ/4 transmission lines 14 and 16 in series between RS and RL. RS and RL have values 65 Ohms and 12.5 Ohms respectively. For optimum impedance matching, λ/4 transmission line 14 has a characteristic impedance of 57 Ohms, and transmission line 16 has a characteristic impedance of 25 Ohms. The series combination of transmission lines introduces a total phase-shift of 180° (it radians) between the output of the RFPS and the input to the discharge electrodes. A detailed description of this and other combinations of fractional transmission line sections for impedance matching is provided in U.S. patent application Ser. No. 12/482,341, filed Jun. 10, 2009, and assigned to the assignee of the present invention.
Yet another example 10D of a prior-art impedance matching circuit including a fractional wavelength transmission line is schematically illustrated in FIG. 1D. Here there are two transmission lines 17 and 19, each thereof having a length of approximately λ/12 in series between RS and RL. This scheme is described in detail in a CERN Report NO. 59-37 entitled “A Convenient Transformer for Matching Co-axial Lines” dated November 1959 and authored by P. Bramham. A similar arrangement is described in a paper “The Twelfth-Wave Matching Transformer”, D. Emerson, QST, Vol. 81, no. 6, June 1997, pp. 43-44.
In the twelfth-wave scheme described in the above-reference papers, in order to match a source impedance ZS to a load impedance ZL the approximately twelfth-wave transmission line lengths (17 and 19 in FIG. 1D) would have a characteristic impedance of ZL and ZS, respectively. Only if ZS were equal to ZL would the transmission line lengths be exactly λ/12 (0.083333λ) long. For practical cases where ZS≠ZL, the precise length of the two transmission-line sections are slightly less than an exact twelfth of a wavelength. According to the Emerson paper, the precise electrical length, l, measured in wavelengths for each transmission line is given by an equation:l={ArcTan [(B/(B2+B+1))1/2]}/2π  (1)where the ArcTan value is in radians and B=ZS/ZL. By way of example, if B were equal to about 4, l would be about 0.0655λ instead of 0.0833λ or approximately 21% shorter in length than a twelfth of a wave. As B moves closure to unity, the length of the line moves closer to λ/12 (0.0833λ).
In the example of FIG. 1D where ZS and ZL are 65 and 50 Ohms respectively, i.e., B=1.3, transmission lines 17 and 19 have a length of 0.08056λ instead of 0.08333λ. In this case, the shorter length imposes a 29 degree phase-shift instead of exactly the 30 degrees that would be imposed by a λ/12 transmission line. Those skilled in the art will recognize that the transmission line lengths referred to above are electrical lengths which include the effect of dielectric constant of insulating material of the transmission lines.
At RFPS frequencies typically used in CO2 gas discharge lasers, for example, between about 40 megahertz (MHz) and about 150 MHz, the size of the discrete LC components in the example of FIG. 1A, is too large, and the length of the ¼ wave transmission lines in the examples of FIGS. 1B and 1C are too long to be compatible with modern, solid-state RFPS packaging technology. By way of example, at an RFPS frequency of 100 MHz, the wavelength in free space is 3 meters. Allowing for a velocity factor in the transmission line of 0.66, the physical transmission line length for an electrical length of one-wavelength is still 1.98 meters, resulting in a λ/4 wavelength line of 0.495 meters, which is still somewhat longer than desirable. The two cascaded (series) λ/12 lines of the arrangement of FIG. 1D, however, would have a total length of less than λ/6 wavelength for a physical length of less than about 0.33 meters, which is more practical for solid-state RFPS packaging.
A particular disadvantage of all of the above-described prior-art impedance matching schemes is an inability to easily fine-adjust the impedance matching circuit to compensate for above discussed impedance matching variations between lasers of a particular model or family. If this disadvantage could be eliminated in the arrangement of FIG. 1D, the resulting arrangement would be very useful in the manufacture of families of CO2 gas discharge lasers.